61 citations · 249 across the 13 of their papers we have counts for
13 papers
Variationally Mimetic Operator Networks
Dhruv Patel, Deep Ray, Michael R. A. Abdelmalik +2
In recent years operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input fu…
Analysis-suitable unstructured T-splines: Multiple extraordinary points per face
Xiaodong Wei, Xin Li, Kuanren Qian +3
Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve a seamless integration between the design and the analysis of thin-walled structures in industrial se…
Quantitative in vivo imaging to enable tumor forecasting and treatment optimization
Guillermo Lorenzo, David A. Hormuth, Angela M. Jarrett +6
Current clinical decision-making in oncology relies on averages of large patient populations to both assess tumor status and treatment outcomes. However, cancers exhibit an inheren…
A comparison of matrix-free isogeometric Galerkin and collocation methods for Karhunen--Loève expansion
Michal Lukasz Mika, René Rinke Hiemstra, Thomas Joseph Robert Hughes +1
Numerical computation of the Karhunen--Loève expansion is computationally challenging in terms of both memory requirements and computing time. We compare two state-of-the-art metho…
The Quad Layout Immersion: A Mathematically Equivalent Representation of a Surface Quadrilateral Layout
Kendrick M. Shepherd, René R. Hiemstra, Thomas J. R. Hughes
Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such…
A matrix-free isogeometric Galerkin method for Karhunen-Loève approximation of random fields using tensor product splines, tensor contraction and interpolation based quadrature
Michal Lukasz Mika, Thomas Joseph Robert Hughes, Dominik Schillinger +2
The Karhunen-Loève series expansion (KLE) decomposes a stochastic process into an infinite series of pairwise uncorrelated random variables and pairwise -orthogonal functions.…
Simulating the spread of COVID-19 via spatially-resolved susceptible-exposed-infected-recovered-deceased (SEIRD) model with heterogeneous diffusion
Alex Viguerie, Guillermo Lorenzo, Ferdinando Auricchio +6
We present an early version of a Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous dif…
Tuned Hybrid Non-Uniform Subdivision Surfaces with Optimal Convergence Rates
Xiaodong Wei, Xin Li, Yongjie Jessica Zhang +1
This paper presents an enhanced version of our previous work, hybrid non-uniform subdivision surfaces [19], to achieve optimal convergence rates in isogeometric analysis. We introd…
The divergence-conforming immersed boundary method: Application to vesicle and capsule dynamics
Hugo Casquero, Carles Bona-Casas, Deepesh Toshniwal +3
We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids.…
A Tchebycheffian extension of multi-degree B-splines: Algorithmic computation and properties
Rene R. Hiemstra, Thomas J. R. Hughes, Carla Manni +2
In this paper we present an efficient and robust approach to compute a normalized B-spline-like basis for spline spaces with pieces drawn from extended Tchebycheff spaces. The exte…
An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS
Karsten Paul, Christopher Zimmermann, Kranthi K. Mandadapu +3
We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff-Love thin shell theory using a…
Polynomial spline spaces of non-uniform bi-degree on T-meshes: Combinatorial bounds on the dimension
Deepesh Toshniwal, Bernard Mourrain, Thomas Hughes
Polynomial splines are ubiquitous in the fields of computer aided geometric design and computational analysis. Splines on T-meshes, especially, have the potential to be incredibly…
An isogeometric finite element formulation for phase transitions on deforming surfaces
Christopher Zimmermann, Deepesh Toshniwal, Chad M. Landis +3
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem i…